Number of Binary tree

Question

Q.Consider a four labeled 1, 2, 3, 4. The number of distinct binary tree are possible such that whose inorder traversal is 1, 2, 3, 4 are _________

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Answer must be 14 right ?

Comments

yes 14

if one order(ie pre order / post order / in order) asked then u can use formula as # BST

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ans is definitely 14.

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This is a made easy question and they have given the answer as 14*4!, they are just confusing people in the last days of GATE preparation, this question is in a full-length test, pathetic. Corrupting knowledge of others.

Answer 1

No. of Binary Trees possible with given Order(Inorder, Preorder, or Postorder) is given by $\binom{2n}{n}/(n+1)$

So Yes Answer is 14